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Max Noether was born in Mannheim in 1844, to a Jewish family of wealthy wholesale hardware dealers. His grandfather, Elias Samuel, had started the business in Bruchsal in 1797. In 1809 the Grand Duchy of Baden established a "Tolerance Edict", which assigned a hereditary surname to the male head of every Jewish family which did not already possess one. Thus the Samuels became the Noether family, and as part of this Christianization of names, their son Hertz (Max's father) became Hermann. Max was the third of five children Hermann had with his wife Amalia Würzburger.[2]

In 1880 he married Ida Amalia Kaufmann, the daughter of another wealthy Jewish merchant family. Two years later they had their first child, named Amalia ("Emmy") after her mother. Emmy Noether went on to become a central figure in abstract algebra. In 1883 they had a son named Alfred, who later studied chemistry before dying in 1918. Their third child, Fritz, was born in 1884. Like Emmy, Fritz Noether also found prominence as a mathematician. Little is known about their fourth child, Gustav Robert, born in 1889. He suffered from continual illness and died in 1928.[4]

Max Noether served as an Ordinarius (full professor) at Erlangen for many years, and died there on 13 December 1921.

Max Noether made major contributions to the theory of algebraic surfaces. Noether's formula is the first case of the Riemann-Roch theorem for surfaces. The Noether inequality is one of the main restrictions on the possible discrete invariants of a surface. The Noether-Lefschetz theorem (proved by Lefschetz) says that the Picard group of a very general surface of degree at least 4 in P3 is generated by the restriction of the line bundleO(1).

Max Noether and Castelnuovo showed that the Cremona group of birational automorphisms of the complex projective plane is generated by the "quadratic transformation"

[x,y,z] ↦ [1/x, 1/y, 1/z]

together with the group PGL(3,C) of automorphisms of P2. Even today, no explicit generators are known for the group of birational automorphisms of P3.